We propose a novel approach for using unsupervised boosting to create an ensemble of generative models, where models are trained in sequence to correct earlier mistakes. Our meta-algorithmic framework can leverage any existing base learner that permits likelihood evaluation, including recent deep expressive models. Further, our approach allows the ensemble to include discriminative models trained to distinguish real data from model-generated data. We show theoretical conditions under which incorporating a new model in the ensemble will improve the fit and empirically demonstrate the effectiveness of our black-box boosting algorithms on density estimation, classification, and sample generation on benchmark datasets for a wide range of generative models.

This paper enlightens the way companies can design Intelligent System to understand their customers' sentiments better to improve their experience, which will help the businesses change their market position. Sentiment analysis is widely acknowledged in the web and social media monitoring. It allows businesses to gain a comprehensive public opinion on the organization and its services. The ability to deduce insights from the text and emoticons from social media is a practice that is now widely adopted by the organizations worldwide. Digital media represents an extensive opportunity for businesses of any industry to acquire the needs, opinions and intent that users share on social media and web.

No, this is not about whether you want your virtual agent to understand English slang, the subjunctive tense in Spanish or even the dozens of ways to say "I" in Japanese. In fact, the programming language you build your bot with is as important as the human language it understands. But how do you differentiate between them? Facebook, Slack and Telegram all support the most popular languages, while API platforms such as Dialogflow, LUIS and wit.ai offer SDKs for the majority. Of course, the caveat should always be to veer toward the language you are most comfortable with, but for those dipping their toe into the programming pond for the first time, a clear winner starts to emerge.

We propose two novel methods for simplifying Gaussian process (GP) models by examining the predictions of a full model in the vicinity of the training points and thereby ordering the covariates based on their predictive relevance. Our results on synthetic and real world data sets demonstrate improved variable selection compared to automatic relevance determination (ARD) in terms of consistency and predictive performance. We expect our proposed methods to be useful in interpreting and understanding complex Gaussian process models.

A vast majority of machine learning algorithms train their models and perform inference by solving optimization problems. In order to capture the learning and prediction problems accurately, structural constraints such as sparsity or low rank are frequently imposed or else the objective itself is designed to be a non-convex function. This is especially true of algorithms that operate in high-dimensional spaces or that train non-linear models such as tensor models and deep networks. The freedom to express the learning problem as a non-convex optimization problem gives immense modeling power to the algorithm designer, but often such problems are NP-hard to solve. A popular workaround to this has been to relax non-convex problems to convex ones and use traditional methods to solve the (convex) relaxed optimization problems. However this approach may be lossy and nevertheless presents significant challenges for large scale optimization. On the other hand, direct approaches to non-convex optimization have met with resounding success in several domains and remain the methods of choice for the practitioner, as they frequently outperform relaxation-based techniques - popular heuristics include projected gradient descent and alternating minimization. However, these are often poorly understood in terms of their convergence and other properties. This monograph presents a selection of recent advances that bridge a long-standing gap in our understanding of these heuristics. The monograph will lead the reader through several widely used non-convex optimization techniques, as well as applications thereof. The goal of this monograph is to both, introduce the rich literature in this area, as well as equip the reader with the tools and techniques needed to analyze these simple procedures for non-convex problems.

In recent years, the inverse Ising problem, i.e. the reconstruction of couplings and external fields of an Ising model from samples of spin configurations, has attracted considerable interest in the physics community [1]. This is due to the fact that Ising models play an important role for data modeling with applications to neural spike data [2, 3], protein structure determination [4], and gene expression analysis [5]. Much effort has been devoted to the development of algorithms for the static inverse Ising problem. This is a nontrivial task, because statistically efficient, likelihood based methods become computationally infeasible by the intractability of the partition function of the model. Hence one has to resort to either approximate inference methods or to other statistical estimators such as pseudo-likelihood methods [6], or the interaction screening algorithm [7]. The situation is somewhat simpler for the dynamical inverse Ising problem, which recently attracted attention [8-13]. If one assumes a Markovian dynamics, the exact normalisation of the spin transition probabilities allows for an explicit computation of the likelihood if one has a complete set of observed data over time. Nevertheless, the model parameters enter the likelihood in a fairly complex way, and the application of more advanced statistical approaches such as Bayesian inference again becomes a nontrivial task. This is especially true for the continuous time kinetic Ising model where the spins are governed by Glauber dynamics [14].

Fuelled by successes in Computer Go, Monte Carlo tree search (MCTS) has achieved widespread adoption within the games community. Its links to traditional reinforcement learning (RL) methods have been outlined in the past; however, the use of RL techniques within tree search has not been thoroughly studied yet. In this paper we re-examine in depth this close relation between the two fields; our goal is to improve the cross-awareness between the two communities. We show that a straightforward adaptation of RL semantics within tree search can lead to a wealth of new algorithms, for which the traditional MCTS is only one of the variants. We confirm that planning methods inspired by RL in conjunction with online search demonstrate encouraging results on several classic board games and in arcade video game competitions, where our algorithm recently ranked first. Our study promotes a unified view of learning, planning, and search.

A general Boltzmann machine with continuous visible and discrete integer valued hidden states is introduced. Under mild assumptions about the connection matrices, the probability density function of the visible units can be solved for analytically, yielding a novel parametric density function involving a ratio of Riemann-Theta functions. The conditional expectation of a hidden state for given visible states can also be calculated analytically, yielding a derivative of the logarithmic Riemann-Theta function. The conditional expectation can be used as activation function in a feedforward neural network, thereby increasing the modelling capacity of the network. Both the Boltzmann machine and the derived feedforward neural network can be successfully trained via standard gradient- and non-gradient-based optimization techniques.

Dynamic networks are a general language for describing time-evolving complex systems, and discrete time network models provide an emerging statistical technique for various applications. It is a fundamental research question to detect the community structure in time-evolving networks. However, due to significant computational challenges and difficulties in modeling communities of time-evolving networks, there is little progress in the current literature to effectively find communities in time-evolving networks. In this work, we propose a novel model-based clustering framework for time-evolving networks based on discrete time exponential-family random graph models. To choose the number of communities, we use conditional likelihood to construct an effective model selection criterion. Furthermore, we propose an efficient variational expectation-maximization (EM) algorithm to find approximate maximum likelihood estimates of network parameters and mixing proportions. By using variational methods and minorization-maximization (MM) techniques, our method has appealing scalability for large-scale time-evolving networks. The power of our method is demonstrated in simulation studies and empirical applications to international trade networks and the collaboration networks of a large American research university.

Monte Carlo methods are essential tools for Bayesian inference. Gibbs sampling is a well-known Markov chain Monte Carlo (MCMC) algorithm, extensively used in signal processing, machine learning, and statistics, employed to draw samples from complicated high-dimensional posterior distributions. The key point for the successful application of the Gibbs sampler is the ability to draw efficiently samples from the full-conditional probability density functions. Since in the general case this is not possible, in order to speed up the convergence of the chain, it is required to generate auxiliary samples whose information is eventually disregarded. In this work, we show that these auxiliary samples can be recycled within the Gibbs estimators, improving their efficiency with no extra cost. This novel scheme arises naturally after pointing out the relationship between the standard Gibbs sampler and the chain rule used for sampling purposes. Numerical simulations involving simple and real inference problems confirm the excellent performance of the proposed scheme in terms of accuracy and computational efficiency. In particular we give empirical evidence of performance in a toy example, inference of Gaussian processes hyperparameters, and learning dependence graphs through regression.